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In order to realize an intermediate band solar cell, which promises high photovoltaic energy conversion efficiency, achieving higher photocurrent while maintaining the cell voltage is essential. We report on a transient photocurrent due to the sequential absorption of photons in a single quantum well by continuously pumping to stimulate interband transitions (from a valence band to an intermediate band) and showing an intersubband transition (from an intermediate band to a conduction band) with a pulsed infrared laser. We demonstrate the extent to which multiple-photon absorption can be achieved in quantum well devices and propose that a quantum well is a suitable candidate for an intermediate band solar cell. From the combination of this and other sequential absorption results, it is clear that enhancing the short lifetime of a carrier in the intermediate band is the next step toward achieving a working intermediate band solar cell. In light of this, we enhance our previous suggestion, the photon ratchet intermediate band solar cell, as a means of increasing the electron lifetime.